Finite Group Databasebeta

← #27205352

Subgroups — #27205352

Order 13184.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268271C211yesmaximal, characteristic
2#20268124C211yesmaximal, characteristic, complemented
3#20268119C211yesmaximal, characteristic, complemented
4#20268095C211yesmaximal, characteristic, complemented
5#20268088C211yesmaximal, characteristic, complemented
6#20267998C211yesmaximal, characteristic, complemented
7#20267993C211yesmaximal, characteristic, complemented
8#20267951C211yesmaximal, characteristic
9#20267951C211yesmaximal, characteristic
10#20267896C211yesmaximal, characteristic, complemented
11#20267889C211yesmaximal, characteristic, complemented
12C4×#13110095C211yesmaximal, characteristic, complemented
13C4×#13110092C211yesmaximal, characteristic, complemented
14#20267852C211yesmaximal, characteristic, complemented
15#541×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C2×#13110095C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×#13110092C2211yescharacteristic
21C4×Dic206C2211yescharacteristic
22C4×Dic206C2211yescharacteristic
23C4×D412C2211yescharacteristic
24C4×D412C2211yescharacteristic
25(C22⋊D103)⋊C4—21no—
26(C22⋊D103)⋊C4—21no—
27#15692979—21no—
28C2×C4⋊Dic103C2211yescharacteristic
29C4⋊C4×D103—21no—
30#15692954C2211yescharacteristic
31#15692954C2211yescharacteristic
32#15692952C2211yescharacteristic
33#15692952C2211yescharacteristic
34C4⋊(C103⋊C8)C2211yescharacteristic
35C4⋊(C103⋊C8)C2211yescharacteristic
36#15692945C2211yescharacteristic
37#15692945C2211yescharacteristic
38#15692945C2211yescharacteristic
39#15692945C2211yescharacteristic
40#15692944C2211yescharacteristic
41#15692944C2211yescharacteristic
42#15692941C2211yescharacteristic
43#15692941C2211yescharacteristic
44C22⋊(C103⋊C8)C2211yescharacteristic
45C22⋊(C103⋊C8)C2211yescharacteristic
46#15692932C2211yescharacteristic
47C4×C103⋊C8C2211yescharacteristic
48C4⋊Q8×C103C2211yescharacteristic
49#126×C103—21no—
50#126×C103—21no—
51#125×C103—21no—
52#125×C103—21no—
53#125×C103C2211yescharacteristic
54C22⋊Q8×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56C4×Q8×C103C2211yescharacteristic
57C4×Q8×C103C2211yescharacteristic
58#117×C103C2211yescharacteristic
59#13110105—22no—
60#13110105—22no—
61C2×Dic206C2311yescharacteristic
62C2×D412C2311yescharacteristic
63C2×C22⋊D103—21no—
64C22×Dic103—21no—
65C2×C4×D103—21no—
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68#13110095—22no—
69#13110095—22no—
70#13110092—22no—
71#13110092—22no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C2×C103⋊C8C2311yescharacteristic
75C2×C103⋊C8C2311yescharacteristic
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81(C2×D103)⋊C4—21no—
82(C2×D103)⋊C4—21no—
83C4×Dic103—21no—
84C4×Dic103—21no—
85C2×Q8×C103C2311yescharacteristic
86C2×Q8×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C4⋊C4×C103—21no—
89C4⋊C4×C103—21no—
90C4⋊C4×C103—21no—
91C4⋊C4×C103—21no—
92C4⋊C4×C103—21no—
93C4⋊C4×C103—21no—
94C4⋊C4×C103—21no—
95C4⋊C4×C103—21no—
96C4⋊C4×C103D411yescharacteristic
97C4⋊C4×C103D411yescharacteristic
98C4⋊C4×C103C2311yescharacteristic
99C4⋊C4×C103C2311yescharacteristic
100C22⋊C4×C103—21no—
101C22⋊C4×C103—21no—
102C22⋊C4×C103D411yescharacteristic
103C22⋊C4×C103D411yescharacteristic
104C42×C103—21no—
105C42×C103—21no—
106C42×C103C2311yescharacteristic
107C42×C103C2311yescharacteristic
108C23×C103C2×D411yescharacteristic
109C22×D103—21no—
110Q8×C103—21no—
111Q8×C103—21no—
112Q8×C103—21no—
113Q8×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103C2×D411yescharacteristic
121C2×C4×C103C2×D411yescharacteristic
122C2×C4×C103C2×D411yescharacteristic
123C2×C4×C103C2×D411yescharacteristic
124C2×C4×C103C2×D411yescharacteristic
125C2×C4×C103C2411yescharacteristic
126C22⋊D103—24no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130C2×Dic103—81no—
131D412—21no—
132D412#4112yes—
133C4×D103—24no—
134C4×D103—81no—
135C4×D103—81no—
136Dic206—21no—
137Dic206#4112yes—
138C103⋊C8—21no—
139C103⋊C8—21no—
140C103⋊C8—21no—
141C103⋊C8—21no—
142C22×C103—21no—
143C22×C103—21no—
144C22×C103—21no—
145C22×C103C22×D411yescharacteristic
146C2×D103—22no—
147C2×D103—41no—
148C2×D103—41no—
149C4×C103—21no—
150C4×C103—21no—
151C4×C103—21no—
152C4×C103—21no—
153C4×C103—21no—
154C4×C103—41no—
155C4×C103—41no—
156C4×C103—41no—
157C4×C103—41no—
158C4×C103C2×#4111yescharacteristic
159C4×C103C2×#4111yescharacteristic
160Dic103—22no—
161Dic103—41no—
162Dic103—41no—
163C2×C103—41no—
164C2×C103#52511yescharacteristic
165C2×C103#57711yescharacteristic
166C2×C103#57811yescharacteristic
167D103—42no—
168#3120—1031nomaximal, Sylow
169C103#312011yescharacteristic, complemented, Sylow
170#541D10311yescharacteristic, complemented
171#520—1031no—
172#484—1031no—
173#483—1031no—
174#479—1031no—
175#478—1031no—
176#462—1031no—
177#461—1031no—
178#452—1031no—
179#452—1031no—
180#441—1031no—
181#440—1031no—
182C4×Q16—1031no—
183C4×SD16—1031no—
184#433—1031no—
185C2×#41—1031no—
186C2×Q16—1031no—
187C2×Q16—1031no—
188C2×SD16—1031no—
189C2×SD16—1031no—
190C4⋊Q8C2×D10311yescharacteristic
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C2×D10311yescharacteristic
196C22⋊Q8C2×D10311yescharacteristic
197C22⋊Q8C2×D10311yescharacteristic
198C4×Q8—1031no—
199C4×Q8—1031no—
200C4×Q8C2×D10311yescharacteristic
201C4×Q8C2×D10311yescharacteristic
202C4×D4—1031no—
203C4×D4—1031no—
204C4×D4—2061no—
205C4×D4—2061no—
206#117—2061no—
207#117C2×D10311yescharacteristic
208C2×C4⋊C4—1031no—
209C2×C4⋊C4—2061no—
210#107—1031no—
211#107—1031no—
212#106—1031no—
213#106—1031no—
214C4⋊C8—1031no—
215C4⋊C8—1031no—
216#103—1031no—
217#103—1031no—
218#103—1031no—
219#103—1031no—
220#103—1031no—
221#103—1031no—
222#102—1031no—
223#102—1031no—
224C22⋊C8—1031no—
225C22⋊C8—1031no—
226#97—1031no—
227C4×C8—1031no—
228#41—2062no—
229#41—2062no—
230C2×Q8—1031no—
231C2×Q8C22×D10311yescharacteristic
232C2×Q8C22×D10311yescharacteristic
233C2×D4—1031no—
234C2×D4—2061no—
235C22×C4—2061no—
236C22×C4—2061no—
237C22×C4—2061no—
238C22×C4—2061no—
239C22×C4C22×D10311yescharacteristic
240Q16—2062no—
241Q16—2062no—
242SD16—2062no—
243SD16—2062no—
244C2×C8—1031no—
245C2×C8—1031no—
246C2×C8—1031no—
247C2×C8—1031no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—1031no—
257C4⋊C4—1031no—
258C4⋊C4—2061no—
259C4⋊C4—2061no—
260C4⋊C4—2061no—
261C4⋊C4C22⋊D10311yescharacteristic
262C4⋊C4C22⋊D10311yescharacteristic
263C4⋊C4C22×D10311yescharacteristic
264C4⋊C4C22×D10311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—2061no—
268C22⋊C4—2061no—
269C22⋊C4C22⋊D10311yescharacteristic
270C22⋊C4C22⋊D10311yescharacteristic
271C42—21no—
272C42—21no—
273C42—2061no—
274C42—2061no—
275C42C22×D10311yescharacteristic
276C42C22×D10311yescharacteristic
277C23—2061no—
278C23C2×C22⋊D10311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—1032no—
284Q8—2061no—
285D4—1032no—
286D4—2064no—
287D4—2061no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—8241no—
295C2×C4—8241no—
296C2×C4—8241no—
297C2×C4—2064no—
298C2×C4—2061no—
299C2×C4—2061no—
300C2×C4—2061no—
301C2×C4C2×C22⋊D10311yescharacteristic
302C2×C4C2×C22⋊D10311yescharacteristic
303C2×C4C2×C22⋊D10311yescharacteristic
304C2×C4C2×C22⋊D10311yescharacteristic
305C2×C4C2×C22⋊D10311yescharacteristic
306C2×C4C23×D10311yescharacteristic
307C8—2061no—
308C8—2061no—
309C8—2061no—
310C8—2061no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—4121no—
315C22—4121no—
316C22—2062no—
317C22C22×C22⋊D10311yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—4121no—
328C4—4121no—
329C4—2062no—
330C4#41×D10311yescharacteristic
331C4#41×D10311yescharacteristic
332C2—41no—
333C2—4122no—
334C2#2026829811yescharacteristic
335C2#2026859911yescharacteristic
336C2#2026860611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#541×C103C2
socleC22×C103C22×D4
prime radicalC2×#13110105C22
hypercenter#541D103
hypocenterC103#3120
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20268124C2semidirect
3. #20268119C2semidirect
4. #20268095C2semidirect
5. #20268088C2semidirect
6. #20267998C2semidirect
7. #20267993C2semidirect
10. #20267896C2semidirect
11. #20267889C2semidirect
12. C4×#13110095C2semidirect
13. C4×#13110092C2semidirect
14. #20267852C2semidirect
15. #541×C103C2semidirect
169. C103#3120semidirect
170. #541D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202682712
#202681242
#202681192
#202680952
#202680882
#202679982
#202679932
#202679512
#202678962
#202678892
C4×#131100952
C4×#131100922
#202678522
#541×C1032
#3120103